Title: Competitive dynamics in a model for river blindness with cross-immunity
Speaker: Horst Thieme, Arizona State University
Date: Wednesday, November 26, 2003, 1:00 pm
Location: Hill Center, Room 260, Rutgers University, Busch Campus, Piscataway, NJ
Abstract:
A mathematical model is formulated for onchocerciasis (river blindness) which involves both the parasites (threadlike worms) afflicting humans (onchocerca volvulus) and cattle (onchocerca ochengi). Both parasites are transmitted by the same flies. Since the flies bite both humans and cattle, every now and then they transmit the parasites into the wrong host where the parasites soon die without causing harm. There is circumstantial evidence that the parasites trigger immune reactions even in the wrong hosts which protects against the other parasite.
The model solutions show the phenomena which are well-known known from the classic Volterra-Lotka two-species competition model. Using persistence theory and monotone dynamical systems with a non-standard order, conditions are determined for competitive exclusion, coexistence, and bistability. It is analyzed how changing the amount of cattle would lead to shifts between these scenarios.
Seminar sponsored by DIMACS/BIOMAPS Seminar Series on Quantitative Biology and Epidemiology.